IMPRODUCT

What it does

IMPRODUCT(inumber1, [inumber2], ...)

IMPRODUCT(inumber1, [inumber2], ...) multiplies complex numbers. The variadic form accepts individual complex values and collections of them.

Try it

=IMPRODUCT("2+i","2-i") returns "5". The imaginary cross terms cancel, while the real term is 4-(-1)=5 because i*i=-1. The returned five is text, ready for another complex function.

Quirks

Complex arguments may be real numbers or text such as "2-3i". Use lowercase i or j; operands in one call must agree on the suffix. The current parser rejects malformed complex text with #NUM! and logical values with #VALUE!. A complex result is text, so ordinary worksheet arithmetic does not automatically treat it as a pair of numeric components. Floating-point reduction order can affect a long calculation even when the corresponding mathematical operation is associative.

How to implement

Parse the two coefficients and suffix before doing arithmetic; use the common complex formatter afterward. Retain suffix consistency, suppress a zero component and omit the coefficient one before the imaginary unit. Formatting and parsing have their own fifteen-significant-digit rules, so testing only the algebra misses observable behaviour.

Start at (1,0) and fold (a,b)*(c,d)=(a*c-b*d,a*d+b*c), retaining both old coefficients until the new pair is computed. The example gives real 4-(-1)=5 and imaginary -2+2=0. The current implementation uses ordinary binary64 component arithmetic. Keep error propagation and traversal of range arguments consistent with the worksheet call model; flattening values without their error policy can change which result is returned.

Rust code

55 improduct "IMPRODUCT" (1, 255) [R "inumber1", R "inumber2"] |s, a, sv| {
    let zs = complexes(s, a, sv)?;
    let product = zs.iter().fold(ParsedComplex::new(1.0, 0.0, None), |acc, z| acc.mul(*z));
    complex_text(Ok(product), &zs)
}

No implementation has been published with a Handbook test suite for this function.

Version differences

The recorded environments below distinguish a reading from a same-input comparison. Counts describe captured inputs in each environment; overlapping captures and comparisons are not totals of unique worksheet calls.

The record contains no same-input comparison between these environments. Reading different inputs on different builds does not establish either a version change or cross-build agreement.

Recorded environments and comparison details.

Alternatives

COMPLEX constructs each input; IMDIV divides; IMPOWER raises one input to a real power.

Named variants

No named variants are recorded yet.